Bacterial-based self-healing concrete (BSHC) is a well-known healing technology which has been investigated for a few decades for its excellent crack healing capacity. The healing performance (HP) of BSHC can be predicted using machine learning (ML) approaches to save the time and cost of laboratory tests, bacteria selection and healing mechanisms adoption.
1. Introduction
Considering that concrete has high compressive strength, excellent workability and a low price, and that it can adapt to a vast range of environmental changes effectively, it has been widely used in the construction industry. Crack formation is an ordinary phenomenon in concrete, mainly caused by the ecological influences that lead to low concrete tensile strength. In general, its tensile strength is only 10–15% of its compressive strength
[1]. Additionally, temperature changes and extreme weather can also lead to changes in the moisture content and internal drying shrinkage in the concrete. In common sense, small cracks less than 0.2 mm are not considered as a severe case
[2]. However, the durability of concrete structures can be dramatically affected by cracks wider than 0.2 mm and, at the same time, internal cracks are not always visible during inspection on a large proportion of concrete structures
[3]. Moreover, the manual method of repairing concrete cracks is restricted due to such pessimistic conditions as the environmental impacts and the limited space of operation
[4]. The cost of repairing cracked concrete structures accounts for half of the construction budget because of the complex operations, which are considered as another problem
[5]. Therefore, to achieve a more effective repairing method and to decrease maintenance funding, an ideal approach should be taken instead of repairing the structure and filling the cracks manually to keep concrete working functionally. A technology named self-healing concrete, which can automatically repair cracks to reduce the maintenance cost and save the environment, was proposed. Self-healing concrete is classified into autogenous healing concrete and agent-based healing concrete
[6]. Autogenous healing concrete can be achieved owing to two main important mechanisms: the continuing hydration of un-hydrated cement particles and the carbonation of calcium hydroxide
[7]. However, the autogenous healing method has its limits, as it is only useful for tiny cracks less than 300 µm. Concerning the trending agent-based healing, it can help concrete heal itself with various healing agents and is therefore considered as the next-generation technology for concrete. Cracks with widths of up to 970 μm can be repaired employing agent-based healing
[8]. The healing agents consist of carriers and core materials with different potentials to heal cracks in concrete. With regard to core materials, bacteria, polymer and expanded materials are employed based on the fact that different healing agents have different healing mechanisms. Thus, BSHC is researched
in this paper.
Machine learning is a kind of artificial intelligence. The aim of ML is to obtain the independent prediction ability by learning from input data sets.
TIn this paper, the HP of BSHC is predicted by employing various ML algorithms. Two researchers have studied the HP prediction of BSHC. In their research, the crack closure percentage of non-ureolytic bacterial healing concrete was predicted by employing ML models. Dosages of bacteria, the initial cracking width and the healing time were considered as the inputs of ML models
[9]. Moreover, the HP of agent-based healing concrete with a lightweight aggregate (LWA) was predicted by utilising an algorithm combining genetic and ANN algorithms. The initial cracking width, the healing time, the weight of the LWA and the LWA with bacteria were selected as the inputs
[10]. It is essential to consider more factors influencing the HP of BSHC due to the complexity of the healing mechanisms.
2.Methodology
2.1 Types of BSHC
Published articles related to BSHC between 2000 and 2021 are collected and analysed
in this paper. According to the record, 15 types of bacteria have been employed for BSHC experiments as shown in
Figure 1. Thereinto,
Cyanobacteria,
Synechococcus,
Prochlorococcus Bacillus alkalinitrilicus,
Bacillus subtilis,
Bacillus cohnii,
Pseudomonas aeruginosa and
Bacillus mucilaginous belong to aerobic bacterial healing concrete.
Bacillus pasteurii,
Bacillus sphaericus,
Bacillus megaterium and
Diaphorobacter nitroreducens can be classified into nitrifying bacterial healing concrete.
Bacillus cereus,
Desulfovibrio brasiliensis and
Desulfovibrio vulgaris can be concluded as ureolytic bacterial healing concrete and sulphate reduction biological mineralisation, respectively. It can be observed from
Figure 1 that seven types of bacteria, i.e.,
Bacillus pasteurii,
Bacillus sphaericus,
Bacillus megaterium,
Bacillus subtilis,
Bacillus cereus,
Bacillus alkalinitrilicus and
Bacillus cohnii, have been employed more commonly. The rest of the bacteria, such as
Cyanobacteria and
Pseudomonas aeruginosa, have been utilised less than twice.
Figure 1. Numbers of publications of bacteria related to BSHC.
2.2 Data Preparation
A total of 797 data sets employed for predicting the HP of BSHC were collected from 14 articles published between 2000 and 2021
[11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Twenty-two variables influencing the HP of BSHC are employed
in this paper to train ML models with the five algorithms. Six variables are used to describe the influencing factors of cementitious materials and water contents: the amount of fine aggregate (FA), the amount of coarse aggregate (CA), types of cement (TC), the amount of cement (CM), the water binder ratio (W/B) and the amount of superplasticiser (S). Furthermore, the eleven variables corelated with bacteria are the types of carriers (C), types of bacteria (B), dosages of bacteria (DB), types of BSHC (TBSHC), types of calcium ions sources (TCIS), dosages of calcium ions (DCI), types of carbon sources (TCS), dosages of carbon (DC), types of nutrients (TN), dosages of nutrients (DN) and dosages of urea (DU). All variables are represented by the mass ratio of concrete. Moreover, the initial cracking date (CD), the initial cracking width (CW), the healing time (HT), the healing condition (HC) and the healing test methods (HTM) are the variables with reference to the healing environment. Finally, the self-healing efficiency is represented by the healing performance (HP) as the unique output.
2.3 Machine Learning Algorithms
TIn this paper, the prediction ability of the five types of ML algorithms, GBR, RF, DNN, DTR and SVR, for predicting the HP of BSHC is studied. To achieve the best prediction ability, here a hyper-parameter tuning method named GSA is utilised to determine the optimal parameters of the ML models
[25].
3. Prediction Ability of ML Models
(a) (b)
Figure 2. Experimental vs. predicted HP for the models: (a) GBR-training; (b) GBR-testing with the corresponding R2 and RMSE.
R
2 and RMSE values are applied to inspect the prediction performance and accuracy of the ML models. The horizontal and vertical axes indicate the experimental and predicted HP, respectively. As is demonstrated in
Figure 2a, b, the GBR model shows a significantly higher R
2 than the other four ML models. The R
2 and RMSE of GBR are 0.956 and 6.756%, respectively. According to the results, the following can be concluded. Firstly, the GBR model is the optimal model for predicting the HP of BSHC due to the highest R
2 (0.956) and lowest RMSE (6.756%). Secondly, the GBR model is reliable because of the similar R
2 results of the training and testing sets, indicating no underfitting or overfitting problem. Thirdly, the RMSE (6.756%) of the GBR model demonstrates that the prediction deviation is low and robust.
(a) (b)
Figure 3. (a) R2 results and (b) RMSE results of GBR models with the 10-fold cross validation for predicting HP of BSHC.
TIn this paper, the prediction ability of GBR is validated by employing 10-fold cross validation. The prediction ability (R2 and RMSE values) of the GBR models validated by different folds of the data sets is shown in Figure 3. Slight differences in R2 and RMSE values of the GBR models can be noticed in Figure 3a,b. For instance, 0.947 is the maximum R2 value of the GBR model at Fold 8, while 0.937 is the minimum R2 value of the GBR model at Fold 1. The rest of the R2 values are maintained at approximately 0.944. Furthermore, the RMSE value dramatically decreases from 6.864% to 6.039% between Fold 1 and Fold 2, followed by a slight growth to 6.210% at Fold 3. Subsequently, it keeps constant at 6.218% until Fold 6. It then fluctuates between 6.067% and 6.218% from Fold 7 to Fold 10.The average R2 and RMSE values of the GBR models with different folds of the data sets are 0.9438 and 6.2342%, respectively. Regarding the R2, RMSE and the statistical results of the GBR models, it can be concluded that the promising prediction ability of the GBR model for predicting the HP of BSHC is reliable.
4. Sensitivity Analysis
Figure 4. sensitivity analysis parameters of the variables.
TIn this paper, the optimal ML model for predicting the HP of BSHC, GBR, is employed for sensitivity analysis (SA) to study the influence of variables on the output from quantitative analysis. With regard to the sensitivity analysis parameter (SAP) results shown in Figure 4, the following aspects can be concluded. Firstly, most of the variables related to cementitious materials and water, such as FA, CM and W/B, show a stronger influence on the HP of BHSC than that of the variables related to bacteria. This is because less water contained in the concrete results in more unreacted cement particles being retained for healing cracks. Furthermore, more FA can lead to the increased demand of water; thus, the HP of concrete with high FA is lower than that of concrete with low FA. It can be concluded that the influence of the variables on the HP of BSHC is CW ≥ water contents > HT > the variables related to bacteria. Secondly, the variables related to the healing environment, such as CW, HT and CD, were recognised as the significant influencing factors of HP[9][10]. However, there was no report to show the influencing degrees of the factors. In t his paper, it can be observed from Figure 4 that the SAP of HT is 7.45%, 12.35% lower than that of CW. Moreover, the SAP of CW is more than three times that of CD. Thirdly, regarding the variables related to bacteria, DB has a higher effect than other variables on the HP of BSHC. The SAPs of the rest of the variables related to bacteria are close, excluding DC and DU, indicating a similar influence on the HP of BSHC. It can be observed from Figure 4 that DC and DU show little influence on the HP of BSHC.